Can't make circular array around an empty
I may have missed the point of your question, or not understood what exactly you wanted to do, but ...

Ignore the empty and don't activate offset. Put the 3D cursor in the centre of the world (0,0,0)

Create a Bezier Circle

In the cylinder's modifier, change Fixed Count to Fit Curve.  Choose the Bezier Circle as the curve.

You'll get a vertical array of however many cylinders you need to fit the circumference of that circle.

With the Array selected, assign a new modifier - Curve - and choose the Bezier Circle as the curve.  I had to set the axis to Z to get what you see in the picture below.